IA Scholar Query: The Hyperspherical Geometry of Community Detection: Modularity as a Distance.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics
https://scholar.archive.org/work/sdqbn7ixmfhgzp7beoeqagvufu
The absence of a conventional association between the cell-cell cohabitation and its emergent dynamics into cliques during development has hindered our understanding of how cell populations proliferate, differentiate, and compete, i.e. the cell ecology. With the recent advancement of the single-cell RNA-sequencing (RNA-seq), we can potentially describe such a link by constructing network graphs that characterize the similarity of the gene expression profiles of the cell-specific transcriptional programs, and analyzing these graphs systematically using the summary statistics informed by the algebraic topology. We propose the single-cell topological simplicial analysis (scTSA). Applying this approach to the single-cell gene expression profiles from local networks of cells in different developmental stages with different outcomes reveals a previously unseen topology of cellular ecology. These networks contain an abundance of cliques of single-cell profiles bound into cavities that guide the emergence of more complicated habitation forms. We visualize these ecological patterns with topological simplicial architectures of these networks, compared with the null models. Benchmarked on the single-cell RNA-seq data of zebrafish embryogenesis spanning 38,731 cells, 25 cell types and 12 time steps, our approach highlights the gastrulation as the most critical stage, consistent with consensus in developmental biology. As a nonlinear, model-independent, and unsupervised framework, our approach can also be applied to tracing multi-scale cell lineage, identifying critical stages, or creating pseudo-time series.Baihan Linwork_sdqbn7ixmfhgzp7beoeqagvufuWed, 28 Sep 2022 00:00:00 GMTDimension matters when modeling network communities in hyperbolic spaces
https://scholar.archive.org/work/nnbgzymq4bcvtpdmbgehysif7a
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations to many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent data with communities. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Since more dimensions also increases the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.Béatrice Désy, Patrick Desrosiers, Antoine Allardwork_nnbgzymq4bcvtpdmbgehysif7aMon, 19 Sep 2022 00:00:00 GMTLearning Representations for Controllable Image Restoration
https://scholar.archive.org/work/pgqdsy2c5fcgtdyxtjpv5mmf3a
Deep Convolutional Neural Networks have sparked a renaissance in all the sub-fields of computer vision. Tremendous progress has been made in the area of image restoration. The research community has pushed the boundaries of image deblurring, super-resolution, and denoising. However, given a distorted image, most existing methods typically produce a single restored output. The tasks mentioned above are inherently ill-posed, leading to an infinite number of plausible solutions. This thesis focuses on designing image restoration techniques capable of producing multiple restored results and granting users more control over the restoration process. Towards this goal, we demonstrate how one could leverage the power of unsupervised representation learning. Image restoration is vital when applied to distorted images of human faces due to their social significance. Generative Adversarial Networks enable an unprecedented level of generated facial details combined with smooth latent space. We leverage the power of GANs towards the goal of learning controllable neural face representations. We demonstrate how to learn an inverse mapping from image space to these latent representations, tuning these representations towards a specific task, and finally manipulating latent codes in these spaces. For example, we show how GANs and their inverse mappings enable the restoration and editing of faces in the context of extreme face super-resolution and the generation of novel view sharp videos from a single motion-blurred image of a face. This thesis also addresses more general blind super-resolution, denoising, and scratch removal problems, where blur kernels and noise levels are unknown. We resort to contrastive representation learning and first learn the latent space of degradations. We demonstrate that the learned representation allows inference of ground-truth degradation parameters and can guide the restoration process. Moreover, it enables control over the amount of deblurring and denoising in the restoration via manipula [...]Givi Meishviliwork_pgqdsy2c5fcgtdyxtjpv5mmf3aFri, 19 Aug 2022 00:00:00 GMTVisual Representation and Recognition without Human Supervision
https://scholar.archive.org/work/etj7jcadgnhqnokklgkgnjbbhq
The advent of deep learning based artificial perception models has revolutionized the field of computer vision. These methods take advantage of the ever-growing computational capacity of machines and the abundance of human-annotated data to build supervised learners for a wide-range of visual tasks. However, the reliance on human-annotated is also a bottleneck for the scalability and generalizability of these methods. We argue that in order to build more general learners (akin to an infant), it is crucial to develop methods that learn without human-supervision. In this thesis, we present our research on minimizing the role of human-supervision for two key problems: Representation and Recognition. Recent self-supervised representation learning (SSL) methods have demonstrated impressive generalization capabilities on numerous downstream tasks. In this thesis, we investigate these approaches and demonstrate that they still heavily rely on the availability of clean, curated and structured datasets. We experimentally demonstrate that these learning capabilities fail to extend to data collected "in-thewild" and hence, expose the need for better benchmarks in self-supervised learning. We also propose novel SSL approaches that minimize this dependence on curated data. Since exhaustively collecting annotations for all visual concepts is infeasible, methods that generalize beyond the available supervision are crucial for building scalable recognition models. We present a novel neural network architecture that takes advantage of the compositional nature of visual concepts to construct image classifiers for unseen concepts. For domains where collecting dense annotations is infeasible, we present an "understanding via associations" paradigm which reformulates the recognition problem as identification of correspondences. We apply this to videos and show that we can densely describe videos by identifying dense spatiotemporal correspondences to other similar videos. Finally, to explore the human ability of generalizing beyond se [...]Senthil Purushwalkam Shwork_etj7jcadgnhqnokklgkgnjbbhqThu, 09 Jun 2022 00:00:00 GMTParameter Space Abstractions for Diversity-based Policy Search
https://scholar.archive.org/work/bv2wyxm6krbqtekhde3ftqtqwy
Many modern systems can be modelled as sequential decision making processes, such as autonomous robots, video game bots, cooling plant control systems, financial trading algorithms, and others. These systems consist of an autonomous agent, making decisions about which actions to execute in an environment. An essential component of the sequential decision making processes, is the agent's policy which defines how the agent makes decisions in every situation. The policy can to be manually defined, or learned from experience, in order to make the agent fully autonomous. In certain cases where the environment dynamics change dramatically, due to moving obstacles or partial agent damage, a single policy may not be sufficient. Therefore, maintaining a diversity of policies is necessary to provide alternatives for the system to function normally. Prior work in the fields of reinforcement learning and quality-diversity shows that a diversity of policies can be learned from interaction experience. Diversity can be achieved either through a single task-conditioned policy or by maintaining a collection of policies. The main limitation of these approaches is that they tend to be sample-inefficient, because they require a large amount of interaction data and because they perform search in a high-dimensional policy parameter space. This thesis presents a novel perspective on diversity-based policy search. The novelty is to model abstractions of the policy parameter space in order to improve the diversity-based policy search. Abstractions are another representation of the search space that offer certain characteristics useful for the policy search process. This topic is split into two parts. The first part of the thesis focuses on approaches towards modelling abstractions over the movement policy parameterisation space, in order to improve policy search in the original policy parameterisation space, in a task-agnostic setting. The abstractions are implemented as forward models, which map the movement policy parameterisation spac [...]Nemanja Rakicevic, Petar Kormushev, Peter Childswork_bv2wyxm6krbqtekhde3ftqtqwyWed, 25 May 2022 00:00:00 GMTJaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials
https://scholar.archive.org/work/iiqwmotycvfdpkabt7yctwdz5q
The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and χ2 distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes' maximal entropy priors are formally expressed in terms of the empirical densities' entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor's orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided.Richard Le Blancwork_iiqwmotycvfdpkabt7yctwdz5qMon, 16 May 2022 00:00:00 GMTBiological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication
https://scholar.archive.org/work/at6kw2swwbd3lcbyocuv47f2oa
Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organise in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of 'subbarrel' patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.John M Brooke, Sebastian S James, Alejandro Jimenez-Rodriguez, Stuart P Wilsonwork_at6kw2swwbd3lcbyocuv47f2oaMon, 28 Mar 2022 00:00:00 GMTOn incorporating inductive biases into deep neural networks
https://scholar.archive.org/work/a2mjyi4mmrgdpovxn722aa64z4
A machine learning (ML) algorithm can be interpreted as a system that learns to capture patterns in data distributions. Before the modern \emph{deep learning era}, emulating the human brain, the use of structured representations and strong inductive bias have been prevalent in building ML models, partly due to the expensive computational resources and the limited availability of data. On the contrary, armed with increasingly cheaper hardware and abundant data, deep learning has made unprecedented progress during the past decade, showcasing incredible performance on a diverse set of ML tasks. In contrast to \emph{classical ML} models, the latter seeks to minimize structured representations and inductive bias when learning, implicitly favoring the flexibility of learning over manual intervention. Despite the impressive performance, attention is being drawn towards enhancing the (relatively) weaker areas of deep models such as learning with limited resources, robustness, minimal overhead to realize simple relationships, and ability to generalize the learned representations beyond the training conditions, which were (arguably) the forte of classical ML. Consequently, a recent hybrid trend is surfacing that aims to blend structured representations and substantial inductive bias into deep models, with the hope of improving them. Based on the above motivation, this thesis investigates methods to improve the performance of deep models using inductive bias and structured representations across multiple problem domains. To this end, we inject a priori knowledge into deep models in the form of enhanced feature extraction techniques, geometrical priors, engineered features, and optimization constraints. Especially, we show that by leveraging the prior knowledge about the task in hand and the structure of data, the performance of deep learning models can be significantly elevated. We begin by exploring equivariant representation learning. In general, the real-world observations are prone to fundamental transformations (e.g., [...]Sameera Ramasinghe, University, The Australian Nationalwork_a2mjyi4mmrgdpovxn722aa64z4Fri, 25 Mar 2022 00:00:00 GMTThis Week's Finds in Mathematical Physics (1-50)
https://scholar.archive.org/work/7dqichdfjraltdavtghiqngis4
These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of n-categories to these subjects. However, there are also digressions into Lie algebras, elliptic curves, linear logic and other subjects. They were typeset in 2020 by Tim Hosgood. If you see typos or other problems please report them. (I already know the cover page looks weird).John C. Baezwork_7dqichdfjraltdavtghiqngis4Mon, 28 Feb 2022 00:00:00 GMTThe Hyperspherical Geometry of Community Detection: Modularity as a Distance
https://scholar.archive.org/work/oth7oz4xhvawdfzdkdp3oiklfq
We introduce a metric space of clusterings, where clusterings are described by a binary vector indexed by the vertex-pairs. We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the angular distance to some modularity vector over the set of clustering vectors. In that sense, modularity-based community detection methods can be seen as a subclass of a more general class of projection methods, which we define as the community detection methods that adhere to the following two-step procedure: first, mapping the network to a point on the hypersphere; second, projecting this point to the set of clustering vectors. We show that this class of projection methods contains many interesting community detection methods. Many of these new methods cannot be described in terms of null models and resolution parameters, as is customary for modularity-based methods. We provide a new characterization of such methods in terms of meridians and latitudes of the hypersphere. In addition, by relating the modularity resolution parameter to the latitude of the corresponding modularity vector, we obtain a new interpretation of the resolution limit that modularity maximization is known to suffer from.Martijn Gösgens, Remco van der Hofstad, Nelly Litvakwork_oth7oz4xhvawdfzdkdp3oiklfqSat, 19 Feb 2022 00:00:00 GMTDoes relativistic cosmology software handle emergent volume evolution?
https://scholar.archive.org/work/x7yffqhbojcttkl2y3sify3mey
Dataset contents: gevcurvtest-53b4464.pdf - article in pdf format flrw_ref_eff_constants.dat - plain text file containing input cosmological parameters used for each simulation run, effective model FLRW cosmological parameters, and expected and simulated final scale factors [gevolution|inhomog]-scale-factors-[LCDM|EdS].dat - plain text tables containing scale factor a(t) values for each software package and reference model gevcurvtest-53b4464-journal.tar.gz - reproducibility source package for producing the article pdf only (without git history) gevcurvtest-53b4464-git.bundle - git source package (unbundle with 'git clone') for reproducibility (allowing for data analysis, replotting and producing the pdf file); inludes git history for the project and for the reproducibility software gevcurvtest-53b4464-snapshot.tar.gz - reproducibility full source package (without results and git history; requires internet access) software-53b4464.tar.gz - set of software source packages (excluding TeX/LaTeX) aiming to allow offline reproducibility (compiling + installing the software used in producing this paper) The authors grant a perpetual, non-exclusive licence to distribute this pdf preprint. All the other materials here are free-licensed (as stated in the individual files and packages).Justyna Borkowska, Boudewijn F. Roukemawork_x7yffqhbojcttkl2y3sify3meyMon, 10 Jan 2022 00:00:00 GMTApocalyptic quantum gravity
https://scholar.archive.org/work/laegdvpe6rgylijt5fhubszepu
The AdS/CFT dictionary connects bulk gravitational physics in an asymptotically anti-de Sitter (AdS) background to the quantum dynamics of a conformally invariant field theory (CFT), defined on the asymptotic boundary. In this thesis, we explore, extend and apply this dictionary for a boundary CFT (BCFT), with a particular focus on the physics of black holes. In a BCFT, a physical boundary is added to the CFT. The simplest dual geometry is an asymptotically AdS spacetime cut off by a physical surface called an end-of-the-world (ETW) brane, homologous to the BCFT boundary. For certain highly symmetric configurations of the BCFT called boundary states, symmetry constrains these ETW branes to a one-parameter family labelled by extrinsic curvature. By placing the CFT boundary in Euclidean time, we construct a one-parameter family of black hole microstates in arbitrary dimension. In two dimensions, we analytically calculate minimal surfaces in the bulk geometry and show that, for some parameter regimes, they pierce the black hole horizon and become disconnected. According to the Hubeny-Rangamani-Ryu-Takayanagi (HRT) formula, these surfaces compute entanglement entropy in the field theory. We find a set of conditions which ensure that the microscopic entanglement entropy, arising from a correlator of twist operators, agrees with the bulk result. In particular, the BCFT reproduces the phase transition between connected and disconnected minimal surfaces. This twist correlator can be immediately evaluated on any conformally related background, giving access to entanglement entropy in a number of other contexts of physical interest. By analytically continuing the thermofield state of a half-line, we arrive at a simple toy model of an evaporating black hole, where the phase transition in minimal surface corresponds to information escaping from the interior. For the BCFT on an interval, this transition can be recast in terms of the performability of a certain set of quantum tasks. We use related techniques to constrain the o [...]David Wakehamwork_laegdvpe6rgylijt5fhubszepuDoes relativistic cosmology software handle emergent volume evolution?
https://scholar.archive.org/work/svsh6sfbnzfgpgalnbt4shkpgy
Dataset contents: gevcurvtest-74ff0f2.pdf - article in pdf format flrw_ref_eff_constants.dat - plain text file containing cosmological parameters used for each simulation run [gevolution|inhomog]-scale-factors-[LCDM|EdS].dat - plain text tables containing scale factor a(t) values for each software package and reference model gevcurvtest-74ff0f2-journal.tar.gz - reproducibility source package for producing the article pdf only (without git history) gevcurvtest-74ff0f2-git.bundle - git source package (unbundle with 'git clone') for reproducibility (allowing for data analysis, replotting and producing the pdf file); inludes git history for the project and for the reproducibility software gevcurvtest-74ff0f2-snapshot.tar.gz - reproducibility full source package (without results and git history; requires internet access) The authors grant a perpetual, non-exclusive licence to distribute this pdf preprint. All the other materials here are free-licensed (as stated in the individual files and packages).Justyna Borkowska, Boudewijn F. Roukemawork_svsh6sfbnzfgpgalnbt4shkpgyTue, 28 Dec 2021 00:00:00 GMTDoes relativistic cosmology software handle emergent volume evolution?
https://scholar.archive.org/work/2kmy5gtgtndjxo7k47kjabva54
Dataset contents: gevcurvtest-74ff0f2.pdf - article in pdf format flrw_ref_eff_constants.dat - plain text file containing cosmological parameters used for each simulation run [gevolution|inhomog]-scale-factors-[LCDM|EdS].dat - plain text tables containing scale factor a(t) values for each software package and reference model gevcurvtest-74ff0f2-journal.tar.gz - reproducibility source package for producing the article pdf only (without git history) gevcurvtest-74ff0f2-git.bundle - git source package (unbundle with 'git clone') for reproducibility (allowing for data analysis, replotting and producing the pdf file); inludes git history for the project and for the reproducibility software gevcurvtest-74ff0f2-snapshot.tar.gz - reproducibility full source package (without results and git history; requires internet access) The authors grant a perpetual, non-exclusive licence to distribute this pdf preprint. All the other materials here are free-licensed (as stated in the individual files and packages).Justyna Borkowska, Boudewijn F. Roukemawork_2kmy5gtgtndjxo7k47kjabva54Tue, 28 Dec 2021 00:00:00 GMTPerformance Variation in Digital Systems:Workload Dependent Modeling and Mitigation
https://scholar.archive.org/work/nkz3konwrrhwrpyz46wr7pvonu
(:Unkn) Unknown, National Technological University Of Athenswork_nkz3konwrrhwrpyz46wr7pvonuWed, 22 Dec 2021 00:00:00 GMTSpherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexity
https://scholar.archive.org/work/y7egudmtz5bhfnclpqs63oosla
The connections of a spatial truss structure play a critical role in the safe and efficient transfer of axial forces between members. For discrete connections, they can also improve construction efficiency by acting as registration devices that lock members in precise orientations. As more geometrically complex spatial trusses are enabled by computational workflows and the demand for material-efficient spanning systems, there is a need to understand the effects of global form on the demands at the connections. For large-scale structures with irregular geometry, customizing individual nodes to meet exact member orientations and force demands may be infeasible; conversely, standardizing all connections results in oversized nodes and a compromise in registration potential. We propose a method for quantifying the complexity of spatial truss designs by the variation in nodal force demands. By representing nodal forces as a geometric object, we leverage the spherical harmonic shape descriptor, developed for applications in computational geometry, to characterize each node by a rotation and translation-invariant fixed-length vector. We define a complexity score for spatial truss design by the variance in the positions of the feature vectors in higher-dimensional space, providing an additional performance metric during early stage design exploration. We then develop a pathway towards reducing complexity by clustering nodes with respect to their feature vectors to reduce the number of unique connectors for design while minimizing the effects of mass standardization.Keith J. Lee, Renaud Danhaive, Caitlin T. Muellerwork_y7egudmtz5bhfnclpqs63ooslaFri, 19 Nov 2021 00:00:00 GMT